Tomographic apparatus

ABSTRACT

The tomographic apparatus of this invention has an attenuation quantity calculating and adjusting unit, a filter length calculating unit, an attenuation correction function calculating unit and a transmission length calculating unit in an arithmetic processing unit. Thus, sectional images with a beam hardening correction can be acquired. The beam hardening correction can be made without using an iterative method. The attenuation correction function calculating unit calculates a correction function by approximating and expressing the correction function by a linear function linking, between two transmission lengths, ratios between measured attenuation quantities for two transmission lengths measured by an X-ray detector, and calculated attenuation physical quantities calculated and adjusted for these transmission lengths.

TECHNICAL FIELD

This invention relates to a tomographic apparatus for use in a CTapparatus, C-arm apparatus or the like.

BACKGROUND ART

X-rays used in a CT apparatus and the like do not have single energy,but are polychromatic X-rays which are a mixture of X-rays with variousenergies. Generally, X-rays with low energy attenuate easily through aninteraction with a transmission substance, compared with X-rays withhigh energy. Therefore, with progress of transmission through asubstance, an energy distribution of X-rays tends to show a high energyside remaining, which does not easily attenuate. As a result, anattenuation coefficient for polychromatic X-rays is not constant, butgradually becomes small. Such phenomenon is called “beam hardeningphenomenon”.

FIG. 7 is a graph schematically showing a correlation between the lengthof a transmission substance (hereinafter abbreviated as “transmissionlength”) and the X-ray detection signal ratio between pre-transmissionand post-transmission (hereinafter defined as “quantity ofattenuation”). In FIG. 7, the horizontal axis represents transmissionlength K while the vertical axis with a logarithmic scale represents thequantity of attenuation. Monochromatic X-rays describe a straight lineas shown in a dotted line in FIG. 7 since detection signal values areexpressed by an exponential function having the transmission length K asthe variable. It is seen, however, that polychromatic X-rays describe acurve which extends in a direction of the less attenuation resultingfrom the longer transmission length K as shown in a solid line in FIG.7.

Generally, in CT reconstruction, a transmission length is converted fromattenuation (that is, the quantity of attenuation) of detection signalvalues, and a distribution of transmission substances is obtained bysolving an inverse problem. If a transmission length is calculated basedon a consideration that attenuation is fixed without taking the beamhardening phenomenon into consideration, the transmission length cannotbe calculated accurately. And CT reconstruction images will have,appearing thereon, artifacts due to a cupping phenomenon, for example,in which CT values lower in the central parts of the reconstructionimages. Therefore, the beam hardening phenomenon must be taken intoconsideration when converting attenuation of the detection signal valuesinto a transmission length.

There is a technique of preparing beforehand a function that can convertattenuation of transmission signal values into a transmission length ofa transmission substance, in which the X-ray transmission length of thetransmission substance is changed variously, and attenuation of eachdetection signal value is measured to be used as a basis. Specifically,where P₀ is a detection signal value before attenuation (that is, adetection signal value before transmission) corresponding to zerotransmission length of the transmission substance, and P is a detectionsignal value after transmission, the quantity of attenuation is P/P₀based on the above definitions, and an attenuation value Ln is derivedfrom a definition Ln=−ln(P/P₀). In is a natural logarithmic function.Using attenuation values measured when the transmission length ischanged variously, and an inverse function is obtained beforehand asapproximate function.

There is also a technique of correcting beam hardening, which adjusts adetection signal energy distribution of a system by measuring data oftwo phantoms and adjusting transmission lengths of two filters (seePatent Document 1, for example).

[Patent Document 1]

Specification of United States Patent Application Publication No.2005/0013414

DISCLOSURE OF THE INVENTION Problem to be Solved by the Invention

However, with the technique of obtaining a transmission length using anapproximate function, there are several unknown coefficients, actualmeasurement is needed for data at least corresponding to the number ofcoefficients as attenuation value measurement data. Thus, there is aproblem that it takes time and effort in data collection, and the burdenis large. With Patent Document 1 noted above, an iterative method isrequired to determine transmission lengths of the two filters.

This invention has been made having regard to the state of the art notedabove, and its object is to provide a tomographic apparatus which cancorrect beam hardening without using an iterative method.

Means for Solving the Problem

To fulfill the above object, this invention provides the followingconstruction.

A tomographic apparatus of this invention is a tomographic apparatus foracquiring a sectional image by tomography, comprising (a) an attenuationphysical quantity measuring device for measuring an attenuation physicalquantity which is a physical quantity relating to attenuation due totransmission of X-rays; (b) an attenuation physical quantity calculatingand adjusting device for calculating and adjusting a calculatedattenuation physical quantity which is the attenuation physical quantityas calculated, by assuming a filter length having a predetermined value;(c) a filter length calculating device for finally calculating andadjusting the calculated attenuation physical quantity by calculatingand determining a filter length which provides an agreement between ameasured attenuation physical quantity for a transmission length whichis the attenuation physical quantity measured by the attenuationphysical quantity measuring device, and a calculated attenuationphysical quantity for the transmission length calculated and adjusted bythe attenuation physical quantity calculating and adjusting device; (d)a correction function calculating device for calculating a correctionfunction for correcting the attenuation physical quantity based onratios between measured attenuation physical quantities for at least twotransmission lengths measured by the attenuation physical quantitymeasuring device and calculated attenuation physical quantities forthese transmission lengths finally calculated and adjusted; and (e) atransmission length calculating device for calculating a transmissionlength of a transmission substance needed for tomography, based on theattenuation physical quantity corrected by the correction functioncalculated by the correction function calculating device, and with aninverse function of a transmission length to attenuation physicalquantity conversion function for conversion into the attenuationphysical quantity; the sectional image being acquired based on thetransmission length calculated by the transmission length calculatingdevice.

According to the tomographic apparatus of this invention, (a) theattenuation physical quantity measuring device measures an attenuationphysical quantity which is a physical quantity relating to attenuationdue to transmission of X-rays. On the other hand, an attenuationphysical quantity is calculable by a predetermined equation. There is adisagreement between the attenuation physical quantity calculated(calculated attenuation physical quantity) and the measured attenuationphysical quantity which is obtained by actual measurement.

Then, (b) the attenuation physical quantity calculating and adjustingdevice calculates and adjusts a calculated attenuation physical quantitywhich is the attenuation physical quantity as calculated, by assuming amaterial not considered, and assuming a filter length having apredetermined value for a filter of this material. (c) The filter lengthcalculating device calculates and determines a filter length whichprovides an agreement between a measured attenuation physical quantityfor a transmission length which is the attenuation physical quantitymeasured by the attenuation physical quantity measuring device, and acalculated attenuation physical quantity for the transmission lengthcalculated and adjusted by the attenuation physical quantity calculatingand adjusting device. The calculated attenuation physical quantity isfinally calculated and adjusted by the filter length determined by thefilter length calculating device in this way. By finally calculating andadjusting the calculated attenuation physical quantity in this way, withthe transmission length used by the above filter length calculatingdevice, no difference occurs between the attenuation physical quantitieshaving the measured value and calculated value. However, with othertransmission lengths, a difference can occur between the attenuationphysical quantites having measured values and calculated values.

Then, (d) the correction function calculating device calculates acorrection function for correcting the attenuation physical quantitybased on ratios between measured attenuation physical quantities for atleast two transmission lengths measured by the attenuation physicalquantity measuring device and calculated attenuation physical quantitiesfor these transmission lengths finally calculated and adjusted. Bycorrecting the attenuation physical quantity with the correctionfunction calculated by the correction function calculating device, theattenuation physical quantity can be calculated accurately with nodifference occurring, with other transmission lengths, between theattenuation physical quantities having the measured value and calculatedvalue. Based on this attenuation physical quantity, (e) the transmissionlength calculating device calculates a transmission length of atransmission substance needed for tomography, with an inverse functionof a transmission length to attenuation physical quantity conversionfunction for conversion into the attenuation physical quantity, wherebythe transmission length can be calculated accurately.

A beam hardening correction can be effected by acquiring a sectionalimage based on this transmission length, thereby to maintain uniformityof the sectional image without being influenced by cupping. The beamhardening correction can be carried out without using an iterativemethod as used in Patent Document 1 described hereinbefore.

In one example of the tomographic apparatus of this invention, thecorrection function calculating device calculates the correctionfunction by approximating and expressing the above correction functionby a linear function linking, between two transmission lengths, theratios between measured attenuation physical quantities for twotransmission lengths measured by the attenuation physical quantitymeasuring device, and calculated attenuation physical quantities forthese transmission lengths calculated and adjusted by the attenuationphysical quantity calculating and adjusting device. With this example,the correction function can be calculated simply, only by substitutingit into a linear expression. Of course, the correction functioncalculating device may calculate the correction function by obtainingthe correction function by a least square method using ratios betweenthe measured attenuation physical quantities for at least twotransmission lengths measured by the attenuation physical quantitymeasuring device, and the calculated attenuation physical quantities forthese transmission lengths calculated and adjusted by the attenuationphysical quantity calculating and adjusting device. In this case, thecorrection function can be obtained with increased accuracy.

In another example of the tomographic apparatus of this invention, boththe filter length calculating device and the correction functioncalculating unit use a measured attenuation physical quantity for onetransmission length of measured attenuation physical quantities for atleast two transmission lengths measured by the attenuation physicalquantity measuring device. With this example, the measurement by theattenuation physical quantity measuring device can be reduced by onetime for the shared use of the measured attenuation physical quantityfor one transmission length. Of course, such shared use is notnecessary. However, a sectional image finally acquired has a majorinfluence of the measured attenuation physical quantities for thetransmission lengths used by the correction function calculating device,but has almost no influence of the measured attenuation physicalquantity for the transmission length used by the filter lengthcalculating device. Thus, the shared use is preferable.

Effects of the Invention

With the tomographic apparatus according to this invention, sectionalimages with a beam hardening correction can be acquired by providing thedevices (a)-(e). The beam hardening correction can be made without usingan iterative method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view and block diagram of an X-ray CT apparatus;

FIG. 2 is a graph schematically showing a correlation between calculatedquantity of attenuation and transmission length, and also showingmeasured quantities of attenuation;

FIG. 3 is a graph for illustrating a case of calculating and determininga filter length after supposing a filter length, and calculating andadjusting a calculated quantity of attenuation;

FIG. 4 is a graph schematically showing a correlation betweenattenuation value and ratio of calculated quantity ofattenuation/measured quantity of attenuation;

FIG. 5 is a flow chart showing a process of tomography (CT datacollection) according to an embodiment;

FIG. 6 is a flow chart showing a process of calibration data collectionin a series of processes including tomography according to theembodiment; and

FIG. 7 is a graph schematically showing a correlation between calculatedquantity of attenuation and transmission length.

DESCRIPTION OF REFERENCES

-   -   2 . . . X-ray detector    -   32 . . . filter length calculating unit    -   33 . . . attenuation quantity calculating and adjusting unit    -   34 . . . attenuation correction function calculating unit    -   35 . . . transmission length calculating unit

EMBODIMENT

An embodiment of this invention will be described hereinafter withreference to the drawings. FIG. 1 is a schematic view and block diagramof an X-ray CT apparatus. FIG. 2 is a schematically graph showing acorrelation between calculated quantity of attenuation and transmissionlength, and also showing measured quantities of attenuation. FIG. 3 is agraph for illustrating a case of calculating and determining a filterlength after supposing a filter length, and calculating and adjusting acalculated quantity of attenuation. FIG. 4 is a graph schematicallyshowing a correlation between attenuation value and ratio of calculatedquantity of attenuation/measured quantity of attenuation.

The X-ray CT apparatus according to this embodiment includes an X-raytube 1 for emitting X-rays, an X-ray detector 2 for detecting the X-raysemitted from the X-ray tube 1 and transmitted through a subject M andthe like, and an arithmetic processing unit 3 for performing variousarithmetic processes based on detection signals of the X-rays detectedby the X-ray detector 2. The X-ray tube 1 and X-ray detector 2 areconstructed revolvable around the subject M by a gantry not shown. Thesubject M for normal CT data collection is a human body, but a phantomsuch as an acrylic plate is used at a time of calibration datacollection.

The X-ray detector 2 detects the X-rays by converting into chargesignals the X-rays emitted from the X-ray tube 1, transmitted through acollimator 4, subject M and a detector cushioning material 5, andincident on a detecting plane, further converting the charge signalsinto electric signals (detection signals), and measuring their values.Based on detection signal values emitted from the X-ray tube 1 anddirectly under the X-ray tube 1 (detection signal values beforetransmission) and detection signal values measured by the X-ray detector2 (detection signal values after transmission), it is possible tomeasure a quantity of attenuation which is a detection signal ratiobetween the X-rays before transmission and after transmission. The X-raydetector 2 corresponds to the attenuation physical quantity measuringdevice in this invention.

The arithmetic processing unit 3 is composed of a central processingunit (CPU) and others. The arithmetic processing unit 3 has atransmission length to attenuation physical quantity conversion function31 for converting into an attenuation physical quantity (a quantity ofattenuation in this embodiment) a transmission length of a transmissionsubstance needed for tomography (CT data collection) at a time ofcalibration data collection, and this transmission length to attenuationphysical quantity conversion function 31 has a filter length calculatingunit 32, an attenuation quantity calculating and adjusting unit 33 andan attenuation correction function calculating unit 34. In addition, thearithmetic processing unit 3 has a transmission length calculating unit35 and a reconstruction processing unit 36 for the time of CT datacollection.

The attenuation quantity calculating and adjusting unit 33, by assuminga filter length having a predetermined value (which is filter lengthK_(imaginary) in this embodiment to be described hereinafter),calculates and adjusts a calculated attenuation physical quantity(calculated quantity of attenuation in this embodiment) which is anattenuation physical quantity (quantity of attenuation in thisembodiment) calculated. The filter length calculating unit 32 finallycalculates and adjusts the calculated attenuation physical quantity(calculated quantity of attenuation in this embodiment) by calculatingand determining the filter length K_(imaginary) which provides anagreement between a measured attenuation physical quantity (measuredquantity of attenuation in this embodiment) for a transmission lengthwhich is an attenuation physical quantity (quantity of attenuation inthis embodiment) measured by the X-ray detector 2 noted above, and thecalculated quantity of attenuation through this transmission lengthcalculated and adjusted by the attenuation quantity calculating andadjusting unit 33 noted above. The attenuation correction functioncalculating unit 34 calculates a correction function for correcting thequantity of attenuation (which is attenuation correction function f(Ln)in this embodiment to be described hereinafter) based on ratios betweenmeasured quantities of attenuation through at least two transmissionlengths measured by the X-ray detector 2 and calculated quantities ofattenuation through these transmission lengths finally calculated andadjusted (ratios of calculated quantities of attenuation/measuredquantities of attenuation).

The transmission length calculating unit 35, based on the quantity ofattenuation corrected by attenuation correction function f(Ln)calculated by the attenuation correction function calculating unit 34noted above, calculates a transmission length of a transmissionsubstance needed for tomography (CT data collection) by the X-ray CTapparatus, with an inverse function of the transmission length toattenuation physical quantity conversion function 31 (attenuationenumeration function Att (K_(phantom)) in this embodiment to bedescribed hereinafter). The reconstruction processing unit 36 acquires asectional image (reconstruction image in FIG. 1) through areconstruction process based on the transmission length calculated bythe transmission length calculating unit 35.

The filter length calculating unit 32 corresponds to the filter lengthcalculating device in this invention. The attenuation quantitycalculating and adjusting unit 33 corresponds to the attenuationphysical quantity calculating and adjusting device in this invention.The attenuation correction function calculating unit 34 corresponds tothe correction function calculating device in this invention. Thetransmission length calculating unit 35 corresponds to the transmissionlength calculating device in this invention. A specific function of eachcomponent in the arithmetic processing unit 3 will be describedhereinafter.

The X-rays generated from the X-ray tube 1 are polychromatic X-rays asnoted above, and their detection signal energy distribution is expressedby X(e) as the function of energy e. Attenuation of the X-rays after theX-rays are generated from the X-ray tube 1 and before they reach thesubject M (e.g. such as through a filter inside the collimator 4) isexpressed by the following equation (1) using a plurality of materialsthrough which the X-rays are transmitted (linear attenuationcoefficients μ_(prei) (e), where i=1, 2, 3, . . . ) and transmissionlengths K_(prei) thereof (where i=1, 2, 3, . . . ). Linear attenuationcoefficients μ_(prei) (e) have known values corresponding to thematerials, and transmission lengths K_(prei) also are known from thelength of the filter inside the collimator 4.

$\begin{matrix}{\left\lbrack {{Math}\mspace{14mu} 1} \right\rbrack\begin{matrix}{{\exp\left\lbrack {- \left\{ {{{\mu_{{pre}\; 1}({\mathbb{e}})} \cdot K_{{pre}\; 1}} + {{\mu_{{pre}\; 2}({\mathbb{e}})} \cdot K_{{pre}\; 2}} + {{\mu_{{pre}\; 3}({\mathbb{e}})} \cdot K_{{pre}\; 3}} + \ldots}\mspace{14mu} \right\}} \right\rbrack}\left( {= {\exp\left\lbrack {- {\sum\limits_{i = 1}^{\;}\;\left\{ {{\mu_{{pre}\; i}({\mathbb{e}})} \cdot K_{{pre}\; i}} \right\}}} \right\rbrack}} \right)} & (1)\end{matrix}} & \;\end{matrix}$

Similarly, attenuation of the X-rays after being transmitted through thesubject M and before they reach the X-ray detector 2 (e.g. through thedetector cushioning material 5) is expressed by the following equation(2) using a plurality of materials through which the X-rays aretransmitted (linear attenuation coefficients μ_(posti) (e), where i=1,2, 3, . . . ) and transmission lengths K_(posti) thereof (where i=1, 2,3, . . . ). Linear attenuation coefficients μ_(pesti) (e) have knownvalues corresponding to the materials, and transmission lengthsK_(posti) also are known from the length of the detector cushioningmaterial 5.

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 2} \right\rbrack & \; \\{{\exp\left\lbrack {- \left\{ {{{\mu_{{post}\; 1}({\mathbb{e}})} \cdot K_{{post}\; 1}} + {{\mu_{{post}\; 2}({\mathbb{e}})} \cdot K_{{post}\; 2}} + {{\mu_{{{post}\; 3}\;}({\mathbb{e}})} \cdot K_{{post}\; 3}} + \ldots}\mspace{14mu} \right\}} \right\rbrack}\left( {= {\exp\left\lbrack {- {\sum\limits_{i = 1}^{\;}\;\left\{ {{\mu_{{post}\; i}({\mathbb{e}})} \cdot K_{{post}\; i}} \right\}}} \right\rbrack}} \right)} & (2)\end{matrix}$

And the conversion from the X-rays to the detection signals in the X-raydetector 2 is expressed by e·[1−exp {−μ_(det)(e)·K_(det)}] using thematerial of the detector (linear energy absorption coefficient μ_(det)(e)) and its thickness K_(det). This linear energy absorptioncoefficient met (e) also has a known value corresponding to thematerial, and thickness K_(det) also is known from the thickness ofX-ray detector 2.

From the above, when there is no subject M, a detection signal energydistribution Signal (e) is expressed by the following equation (3) usingequation (1) and equation (2) above.

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 3} \right\rbrack & \; \\\begin{matrix}{{{signal}({\mathbb{e}})} = {{X({\mathbb{e}})} \cdot}} \\{{\exp\left\lbrack {- \left\{ {{{\mu_{{pre}\; 1}({\mathbb{e}})} \cdot K_{{pre}\; 1}} + {{\mu_{{pre}\; 2}({\mathbb{e}})} \cdot K_{{pre}\; 2}} + {{\mu_{{{pre}\; 3}\;}({\mathbb{e}})} \cdot K_{{pre}\; 3}} + \ldots} \right\}} \right\rbrack} \cdot} \\{{\exp\left\lbrack {- \left\{ {{{\mu_{{post}\; 1}({\mathbb{e}})} \cdot K_{{post}\; 1}} + {{\mu_{{post}\; 2}({\mathbb{e}})} \cdot K_{{post}\; 2}} + {{\mu_{{{post}\; 3}\;}({\mathbb{e}})} \cdot K_{{post}\; 3}} + \ldots} \right\}} \right\rbrack} \cdot} \\{{\mathbb{e}} \cdot \left\lbrack {1 - {\exp\left\{ {{- {\mu_{\det}({\mathbb{e}})}} \cdot K_{\det}} \right\}}} \right\rbrack} \\{= {{X({\mathbb{e}})} \cdot}} \\{{\exp\left\lbrack {- {\sum\limits_{i = 1}^{\;}\;\left\{ {{\mu_{{pre}\; i}({\mathbb{e}})} \cdot K_{{pre}\; i}} \right\}}} \right\rbrack} \cdot} \\{{\exp\left\lbrack {- {\sum\limits_{i = 1}^{\;}\;\left\{ {{\mu_{{post}\; i}({\mathbb{e}})} \cdot K_{{post}\; i}} \right\}}} \right\rbrack} \cdot} \\{{\mathbb{e}} \cdot \left\lbrack {1 - {\exp\left\{ {{- {\mu_{\det}({\mathbb{e}})}} \cdot K_{\det}} \right\}}} \right\rbrack}\end{matrix} & (3)\end{matrix}$

In equation (3) above, the conversion from the X-rays to the detectionsignals in the X-ray detector 2 may be calculated frome·[1−exp{−μ′_(det) (e)·K_(det)}]·μ_(det) (e)/μ′_(det) (e) using linearattenuation coefficient μ′_(det) (e) of the material of the detector,instead of e·[1−exp{−μ_(det) (e)·K_(det)}]. This linear attenuationcoefficient μ′_(det) (e) also has a known value corresponding to thematerial.

If the detection signal energy distribution Signal (e) could becalculated accurately, attenuation of the X-rays in the material of thesubject M (linear attenuation coefficient μ_(phantom)(e)) and itstransmission length K_(phantom) would be expressed byexp[−{μ_(phantomn)(e)·K_(phantom)}]. Linear attenuation coefficientμ_(phantom) (e) has a known value corresponding to the material. Thequantity of attenuation P/P₀ of the detection signals at that time canbe calculated accurately with the Att (K_(phantom)) function(hereinafter called “attenuation enumeration function”) in the followingequation (4).

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 4} \right\rbrack & \; \\{{{Att}\left( K_{phantom} \right)} = \frac{\int{{{{Signal}({\mathbb{e}})} \cdot {\exp\left\lbrack {- \left\{ {{\mu_{phantom}({\mathbb{e}})} \cdot K_{phantom}} \right\}} \right\rbrack}}{\mathbb{d}{\mathbb{e}}}}}{\int{{{Signal}({\mathbb{e}})}{\mathbb{d}{\mathbb{e}}}}}} & (4)\end{matrix}$

However, when the quantity of attenuation P/P₀ is measured by the X-raydetector 2, since the materials through which the X-ray are transmittedinclude also a material not taken into consideration, as shown in FIG.2, there is a disagreement between the measured quantity of attenuation(see black dots in FIG. 2) and the calculated quantity of attenuationP/P₀ (=attenuation enumeration function Att (K_(phantom))) (solid linein FIG. 2) derived from the above equation (4).

Then, the detection signal energy distribution Signal (e) is changed bynewly assuming one type of material (linear attenuation coefficientμ_(imaginary) (e)) not taken into consideration and assuming thattransmission has taken place through its length K_(imagmary).Specifically, an appropriate assumption is made of any one type ofmaterial selected from materials such as aluminum (Al), copper (Cu) andso on, for example, and linear attenuation coefficient μ_(imaginary) (e)of the assumed material is assumed. Or an assumption may be made bydefining linear attenuation coefficient μ_(imaginary) (e) of animaginary material which does not actually exist. Linear attenuationcoefficient μ_(imaginary) (e) has a known value corresponding to theassumed material. In the following equation (5), Signal (e) of theright-hand side indicates the energy distribution derived from equation(3) above, and Signal (e) of the left-hand side indicates the energydistribution changed newly. That is, detection signal energydistribution Signal (e) is changed by substituting Signal (e) derivedfrom equation (3) above into the right-hand side of the followingequation (5), substituting the assumed linear attenuation coefficientμ_(imaginary) (e) and filter length K_(imaginary) into the right-handside of the following equation (5), and obtaining a value of Signal (e)of the left-hand side.[Math 5]signal(e)=signal(e)·exp[−{μ_(imaginary)(e)·K _(imaginary)}]  (5)

The attenuation quantity calculating and adjusting unit 33 of thearithmetic processing unit 3 assumes a filter length K_(imaginary)having an arbitrary value according to equation (5) above, and changesdetection signal energy distribution Signal (e) to the left-hand side inequation (5) above. And the attenuation quantity calculating andadjusting unit 33 calculates and adjusts the calculated quantity ofattenuation by calculating attenuation enumeration function Att(K_(phantom)) for transmission length K_(phantom) of the subject M fromequation (4) above using the changed detection signal energydistribution Signal (e). Specifically, as shown in FIG. 3, filter lengthK_(imaginary) is changed to bring into agreement the quantity ofattenuation through a certain transmission length K₁ measured by theX-ray detector 2 (measured quantity of attenuation) (see the whitetriangle in FIG. 3), and calculated quantity of attenuation Att (K₁)through the transmission length K₁ (see the black dot on the solid linein FIG. 3). With the setting change to the filter length K_(imaginary),detection signal energy distribution Signal (e) also is changed byequation (5) above, With this, the calculated quantity of attenuationAtt (K₁) also is adjusted by equation (5) and equation (4) above, andthe calculated quantity of attenuation Att (K₁) adjusted approaches in adirection indicated by an arrow in FIG. 3 to agree with the measuredquantity of attenuation (see the black dot on the two-dot chain line inFIG. 3). The filter length calculating unit 32 of the arithmeticprocessing unit 3 calculates and determines this filter lengthK_(imaginary) when an agreement is attained.

Thus, by calculating filter length K_(imaginary) which provides anagreement between the measured quantity of attenuation through the abovetransmission length and the calculated quantity of attenuation throughthis transmission length, the attenuation quantity calculating andadjusting unit 33 finally calculates and adjusts attenuation enumerationfunction Att (K_(phantom)) for transmission length K_(phantom) from thegraph of the solid line in FIG. 3 to the graph of the two-dot chain linein FIG. 3. Since the measured quantity of attenuation and (calculatedand adjusted) calculated quantity of attenuation Att (K₁) through theabove transmission length K₁ are brought into agreement by this finalcalculation and adjustment, no difference occurs between quantities ofattenuation in measured value and calculated value.

Once the attenuation quantity calculating and adjusting unit 33 finallycalculates and adjusts attenuation enumeration function Att(K_(phantom)) for transmission length K_(phantom) by calculating filterlength K_(imaginary) in this way, no difference will occur between thequantities of attenuation in measured value and calculated value for theabove transmission length K₁. However, even if attenuation enumerationfunction Att (K_(phantom)) is finally calculated and adjusted, when acomparison is actually made with measurements, differences do occur,depending on conditions, between the quantities of attenuation inmeasured value and calculated value for other transmission lengths thantransmission length K₁. As shown in FIG. 4, with a difference occurringwith a change of an attenuation value being expressed by a ratio betweencalculated quantity of attenuation and measured quantity of attenuation,since calculated quantity of attenuation Att (K₁) for the abovetransmission length K₁ is finally calculated and adjusted to agree withthe measured quantity of attenuation, the ratio between calculatedquantity of attenuation and measured quantity of attenuation is “1” andthere is no difference therebetween for natural logarithmic value [−ln{Att (K₁)}] of calculated quantity of attenuation Att (K₁) throughtransmission length K₁ (that is, calculated attenuation value fortransmission length K₁). However, it will be seen from the graph of FIG.4 that a difference occurs in proportion to a distance of theattenuation value from the calculated attenuation value for transmissionlength K₁, which varies by a linear function as a whole.

Then, an attenuation correction function which shows this ratio betweenof calculated quantity of attenuation and measured quantity ofattenuation is expressed here by function f(Ln) of calculatedattenuation value Ln. Ratios between measured quantities of attenuationthrough at least two transmission lengths measured by the X-ray detector2, and calculated quantities of attenuation through these transmissionlengths finally calculated and adjusted, i.e. ratios between calculatedquantity of attenuation and measured quantity of attenuation, areassumed to be (Ln1, rate1), (Ln2, rate2) and so on to correspond tocalculated attenuation values Ln, respectively.

In this embodiment, the X-ray detector 2 measures quantities ofattenuation through two transmission lengths K₁, K₂, and descriptionwill be made assuming that one of them, i.e. the measured quantity ofattenuation through transmission length K₁, is used when the filterlength calculating unit 32 noted hereinbefore calculates and determinesfilter length K_(imaginary). That is, in this embodiment, the measuredquantities of attenuation through the two transmission lengths K₁, K₂are used when the attenuation correction function calculating unit 34,described hereinafter, of the arithmetic processing unit 3 calculatesattenuation correction function f(Ln), and one of them, i.e. themeasured quantity of attenuation through transmission length K₁ is usedwhen the filter length calculating unit 32 calculates and determinesfilter length K_(imaginary).

The attenuation correction function calculating unit 34 of thearithmetic processing unit 3 sets (Ln1, rate1), (Ln2, rate2)respectively corresponding to calculated attenuation values Ln, whichare ratios between the measured quantities of attenuation through thetwo transmission lengths K₁, K₂ measured by the X-ray detector 2, andcalculated quantities of attenuation Att (K₁), Att (K₂) through thesetransmission lengths K₁, K₂ finally calculated and adjusted (i.e. ratiosbetween calculated quantity of attenuation and measured quantity ofattenuation). That is, in this embodiment, since the ratio of calculatedquantity of attenuation Att (K₁)/measured quantity of attenuationthrough transmission length K₁ is rate1, and calculated quantity ofattenuation Att (K₁) through transmission length K₁ is calculated andadjusted to agree with the measured quantity of attenuation, the ratiorate 1 of calculated quantity of attenuation Att (K₁)/measured quantityof attenuation through transmission length K₁ is “1”. The calculatedattenuation value for transmission length K₁ is Ln1, and calculatedattenuation value Ln1 for transmission length K₁ is expressed by “−ln{Att (K₁)}”. The ratio of calculated quantity of attenuation Att(K₂)/measured quantity of attenuation through transmission length K₂ israte2, and calculated attenuation value Ln2 through transmission lengthK₂ is expressed by “−ln {Att (K₂)}”.

As described above, attenuation correction function f(Ln) differing fromcalculation attenuation value Ln1 (=−ln {Att (K₁)}) for transmissionlength K₁ is expressed by a linear function. That is, attenuationcorrection function f(Ln) is expressed by a linear expression linking(Ln1, rate1), (Ln2, rate2) for transmission lengths K₁, K₂. And when thecalculated attenuation value is “0”, attenuation correction functionf(Ln) can be expressed by the following equation (6) in order to returnthe ratio of calculated quantity of attenuation/measured quantity ofattenuation to “1”. τ is an appropriate time constant for returning theratio of calculated quantity of attenuation/measured quantity ofattenuation to “1” when the calculated attenuation value is “0”. Thistime constant τ may be determined by measuring a quantity of attenuationcorresponding to an attenuation value close to “0” and using themeasured quantity of attenuation.

$\begin{matrix}\left\lbrack {{Math}\mspace{14mu} 6} \right\rbrack & \; \\{{f({Ln})} = {1 + {\left\{ {1 - {\exp\left( {- \frac{Ln}{\tau}} \right)}} \right\} \cdot \left\{ {{\frac{{{rate}\; 2} - {{rate}\; 1}}{{{Ln}\; 2} - {{Ln}\; 1}} \cdot \left( {{Ln} - {{Ln}\; 1}} \right)} + {{rate}\; 1} - 1} \right\}}}} & (6)\end{matrix}$

The term of the exponential function in equation (6) above is set, whenthe calculated attenuation value is “0”, to draw a curve, as shown inFIG. 4, from calculated attenuation value at “0” to calculatedattenuation value Ln1 for transmission length K₁ in order to return theratio of calculated quantity of attenuation/measured quantity ofattenuation to “1”. That is, a curve is drawn as shown in FIG. 4, withthe term of the exponential function being effective since theattenuation value is small from the calculated attenuation value at “0”to calculated attenuation value Ln1 for transmission length K₁. As aresult, when the calculated attenuation value is “0”, attenuationcorrection function f(Ln)=1 by substituting Ln=0 into equation (6)above, and thus the ratio of calculated quantity of attenuation/measuredquantity of attenuation can be returned to “1”. On the other hand, theattenuation value becomes large when calculated attenuation value Ln1for transmission length K₁ is exceeded, as a result of which the term ofthe exponential function can substantially be disregarded, andattenuation correction function f(Ln) is expressed by a linear function.

After the attenuation correction function calculating unit 34 calculatesattenuation correction function f(Ln) from equation (6) above, thequantity of attenuation is corrected using this attenuation correctionfunction f(Ln). That is, attenuation enumeration function Att(K_(phantom)) for transmission length K_(phantom), i.e. the quantity ofattenuation through each transmission length K_(phantom), is correctedby dividing attenuation enumeration function Att (K_(phantom)) finallycalculated and adjusted by the quantity of attenuation calculating andadjusting unit 33, by attenuation correction function f(Ln) (=f[−ln {Att(K_(phantom))}]) derived from equation (6) above. Thus, the quantity ofattenuation can be calculated accurately without generating differencesfor other transmission lengths. The solid line in FIG. 4 is attenuationcorrection function f(Ln). The white rhombuses on the solid line in FIG.4 are differences. The black rectangles in FIG. 4 are differences aftercorrection. As seen from FIG. 4, the differences after correction arepresent substantially on “1” as the ratio of calculated quantity ofattenuation/measured quantity of attenuation despite variations in theattenuation value, which shows that the differences are eliminated.

This corrected quantity of attenuation has a value dependent on thematerial (linear attenuation coefficient μ_(phantom) (e)) andtransmission length K_(phantom) of a phantom (e.g. acrylic plate) usedas subject M at a time of calibration data collection. Then, in order todetermine a transmission length of water which is a transmissionsubstance needed for tomography (i.e. at a time of CT data collection)by the X-ray CT apparatus, a corrected attenuation physical quantity fortransmission length K_(phantom) of water (corresponding to thetransmission length to attenuation physical quantity conversion function31 in FIG. 1) can be calculated by using the linear attenuationcoefficient of water instead of μ_(phantom) of the phantom material inequation (4) above using the same value as filter length K_(imagmary),and from the division made by equation (6) above. The linear attenuationcoefficient has a known value corresponding to the transmissionsubstance as noted hereinbefore.

Also other transmission lengths than water needed for tomography (CTdata collection) can be converted to attenuation physical quantities bythe transmission length to attenuation physical quantity convertionfunction 31. Then, conversely, the transmission length of water iscalculated from the attenuation physical quantity by the inversefunction of transmission length to attenuation physical quantityconvertion function 31.

From attenuation physical quantities matched with respectivetransmission lengths, a look-up table having the attenuation physicalquantities as input and the transmission lengths as output is preparedfor obtaining the inverse function of transmission length to attenuationphysical quantity convertion function 31. Transmission lengthK_(phantom) can be calculated accurately since transmission lengthK_(phantom) is determined using the quantity of attenuation calculatedaccurately.

The transmission length calculating unit 35 of the arithmetic processingunit 9 calculates transmission length K_(phantom) of water, using thelook-up table, from the physical attenuation quantity.

As is clear from the above description, the quantity of attenuation andattenuation value correspond to the attenuation physical quantity inthis invention. The filter length K_(imaginary) corresponds to thefilter length in this invention. Attenuation correction function f(Ln)corresponds to the correction function in this invention. The result ofthe division of attenuation enumeration function Att (K_(phantom)) byattenuation correction function f(Ln) corresponds to the transmissionlength to attenuation physical quantity conversion function in thisinvention.

Next, a series of processes including tomography according to thisembodiment will be described with reference to FIGS. 5 and 6. FIG. 5 isa flow chart showing a process of tomography (CT data collection)according to the embodiment. FIG. 6 is a flow chart showing a process ofcalibration data collection in the series of processes includingtomography according to the embodiment.

(Step T1) Calculation of Transmission Length

The transmission length calculating unit 35 calculates a transmissionlength of a transmission substance needed for tomography (CT datacollection). For this purpose, calibration data is collected in thefollowing steps S1-S6.

(Step S1) Calculation of Detection Signal Energy Distribution

A detection signal energy distribution Signal (e) is calculated usingequation (3) above from sensitivity characteristics of the X-raydetector 2, X-ray spectrum and so on. This detection signal energydistribution Signal (e) is a parameter determined beforehand. Once thedetection signal energy distribution Signal (e) is determinedbeforehand, it is not necessary to execute step S1 each time.

(Step S2) Measurement of Quantities of Attenuation

Phantom radiography is carried out for calibration data collection,using a phantom (acrylic plate or the like) as subject M. Specifically,quantities of attenuation are measured by the X-ray detector 2 bychanging the transmission length each time. Regarding the quantities ofattenuation measured as measured quantities of attenuation, the measuredquantities of attenuation through at least two transmission lengthsmeasured by the X-ray detector 2 are acquired. In this embodiment, themeasured quantities of attenuation through two transmission lengths K₁,K₂ are acquired as noted hereinbefore.

(Step S3) Calculation of Filter Length

The attenuation quantity calculating and adjusting unit 33 changes thedetection signal energy distribution Signal (e) in step S1 usingequation (5) above, by assuming a material not taken into considerationand considering that a filter of that material is penetrated throughappropriate filter length K_(imaginary). The attenuation quantitycalculating and adjusting unit 33 calculates and adjusts the calculatedquantity of attenuation by calculating attenuation enumeration functionAtt (K_(phantom)) from equation (4) above using the changed detectionsignal energy distribution Signal (e). And the filter length calculatingunit 32 calculates filter length K_(imaginary) which provides anagreement between the measured quantity of attenuation throughtransmission length K₁ measured by the X-ray detector 2 in step S2 andthe calculated quantity of attenuation Att (K₁) through thattransmission length K₁.

(Step S4) Calculation and Adjustment of Attenuation Enumeration Function

Thus, the attenuation quantity calculating and adjusting unit 33 finallycalculates and adjusts attenuation enumeration function Att(K_(phantom)) by calculating filter length K_(imaginary) in step S3.

(Step S5) Calculation of Attenuation Correction Function

The attenuation correction function calculating unit 34 calculatesattenuation correction function f(Ln) using equation (6) above based onthe ratios between the measured quantities of attenuation through thetwo transmission lengths K₁, K₂ measured by the X-ray detector 2 in stepS2, and calculated quantities of attenuation Att (K₁), Att (K₂) throughthese transmission lengths K₁, K₂ finally calculated and adjusted (stepS4).

(Step S6) Calculation of Inverse Function Information

The linear attenuation coefficient of water which is the transmissionsubstance needed for tomography is substituted into equation (4) aboveto calculate and adjust the quantity of attenuation through thetransmission length of water, and a corrected quantity of attenuation iscalculated by correcting the quantity of attenuation using attenuationcorrection function f(Ln) calculated in step S6. Corrected quantities ofattenuation are calculated, through the same procedure, for othertransmission lengths of that transmission substance. Prior to CT imaging(i.e. tomography by the X-ray CT apparatus), a look-up table forobtaining an inverse function (i.e. inverse function information) isprepared as having the corrected quantities of attenuation and eachtransmission length K_(phantom) in a corresponding relationship. Once itis prepared, it is not necessary to repeat it before each CT imaging.

(Step T1) Calculation of Transmission Length

A transmission length is obtained from a quantity of attenuation orattenuation value using the look-up table prepared in step S6.

(Step T2) Reconstruction Process

And based on this transmission length, the reconstruction processingunit 36 acquires a sectional image (reconstruction image) by solving theinverse problem, carrying out a reconstruction process, and determininga distribution of transmission substances.

A beam hardening correction can be effected by acquiring a sectionalimage based on the transmission length accurately calculated in step T1,thereby to maintain uniformity of the sectional image without beinginfluenced by cupping. The beam hardening correction can be carried outwithout using an iterative method as used in Patent Document 1 describedhereinbefore. Compared with the conventional technique of determining atransmission length using an approximation function, only the number ofdeterminations by the X-ray detector 2 matters, which produces also theeffect of reducing the time and effort for collecting data andlightening the burden.

In this embodiment, as described above, the attenuation correctionfunction calculating unit 34 calculates attenuation correction functionf(Ln) by approximating and expressing attenuation correction functionf(Ln) by a linear function linking, as (Ln1, rate1), (Ln2, rate2)between two transmission lengths K₁, K₂, the ratios between measuredquantities of attenuation through the two transmission lengths K₁, K₂measured by the X-ray detector 2, and calculated quantities ofattenuation Att (K₁), Att (K₂) through these transmission lengths K₁,K₂. In this case, attenuation correction function f(Ln) can becalculated simply, only by substituting it into the linear expression.

In this embodiment, as described above, both the filter lengthcalculating unit 32 and attenuation correction function calculating unit34 use the measured quantity of attenuation through one transmissionlength K₁ of the measured quantities of attenuation through at least twotransmission lengths K₁, K₂ measured by the X-ray detector 2. In thiscase, the measurement by the X-ray detector 2 can be reduced by one timefor the shared use of the measured quantity of attenuation through onetransmission length K₁.

This invention is not limited to the foregoing embodiment, but may bemodified as follows:

(1) In the foregoing embodiment, the attenuation physical quantityprocessed by the attenuation physical quantity measuring device (X-raydetector 2 in the embodiment) and the attenuation physical quantitycalculating and adjusting device (attenuation quantity calculating andadjusting unit 33 in the embodiment) is the quantity of attenuationexpressed by the detection signal ratio between X-rays beforetransmission and after transmission. However, there is no limitation asto the attenuation physical quantity, as long as it is a parameterrelating to attenuation as illustrated by the attenuation value which isa natural logarithmic value of the quantity of attenuation. There is nolimitation as to also the attenuation physical quantity processed by theattenuation physical quantity measuring device and attenuation physicalquantity calculating and adjusting device.

(2) In the foregoing embodiment, the correction function (attenuationcorrection function in the embodiment) is calculated using the measuredattenuation physical quantities (measured quantities of attenuation inthe embodiment) for two transmission lengths K₁, K₂ measured by theX-ray detector 2. However, as long as the measured attenuation physicalquantities for at least two transmission lengths are used, thecorrection function may be calculated using measured attenuationphysical quantities for three or more transmission lengths, for example.There is no limitation as to the number of measured attenuation physicalquantities used as long as they are plural.

(3) In the foregoing embodiment, the correction function is calculatedby approximating and expressing the correction function (attenuationcorrection function in the embodiment) with a linear function in thelinear expression linking (Ln1, rate1), (Ln2, rate2) for twotransmission length K₁, K₂ measured by the X-ray detector 2, but this isnot limitative. The correction function may be calculated by obtainingthe correction function by a least square method using (Ln1, rate1),(Ln2, rate2), (Ln2, rate3) for at least two transmission lengths (e.g.three transmission lengths K₁, K₂, K₃) measured by the X-ray detector 2.In this case, the correction function can be obtained with increasedaccuracy.

(4) In the foregoing embodiment, both the filter length calculating unit32 and attenuation correction function calculating unit 34 use themeasured quantity of attenuation through one transmission length K₁ ofthe measured quantities of attenuation through at least two transmissionlengths K₁, K₂ . . . measured by the X-ray detector 2, but such shareduse is not absolutely necessary. However, where, for example, a measuredquantity of attenuation through a transmission length is not shared,such that the filter length calculating unit 32 uses the measuredquantity of attenuation through transmission length K₁ and theattenuation correction function calculating unit 34 uses the measuredquantities of attenuation through two transmission lengths K₂, K₃, asectional image finally acquired has a major influence of the measuredquantities of attenuation through transmission lengths K₂, K₃ used bythe attenuation correction function calculating unit 34, but has almostno influence of the measured quantity of attenuation throughtransmission length K₁ used by the filter length calculating unit 32.Thus, a shared use as in the embodiment is preferable.

(5) In the foregoing embodiment, the tomographic apparatus is an X-rayCT apparatus. However, this invention is applicable also to an apparatuswhich carries out tomography by means of a C-arm. Thus, there is nolimitation as to the tomography apparatus to which this invention isapplied.

The invention claimed is:
 1. A tomographic apparatus for acquiring asectional image, comprising: an attenuation quantity measuring devicefor measuring an X-ray attenuation quantity by emitting X-rays to aphantom having a known thickness; an attenuation quantity calculatingdevice for calculating an X-ray attenuation quantity assuming X-rays areemitted to a filter formed of a predetermined material having the knownthickness; a correction quantity calculating device for calculating as acorrection quantity a ratio between the measured X-ray attenuationquantity and the calculated X-ray attenuation quantity; a correctionfunction calculating device for calculating, based on correctionquantities calculated with a plurality of known thicknesses, acorrection function showing a relationship between the measuredattenuation quantity and the correction quantity; and a transmissionlength calculating device for calculating a transmission length byacquiring from the correction function a correction quantitycorresponding to an X-ray attenuation quantity measured by emittingX-rays to a subject, correcting the X-ray attenuation quantity measuredby emitting X-rays to the subject with the acquired correction quantity,and converting the corrected X-ray attenuation quantity into a thicknessof the predetermined material; the sectional image being acquired basedon the transmission length.
 2. The tomographic apparatus according toclaim 1, wherein the correction function calculating device calculatesthe correction function by approximating and expressing the correctionfunction by a linear function linking, between two transmission lengths,the ratios between measured attenuation physical quantities for twotransmission lengths measured by the attenuation physical quantitymeasuring device, and calculated attenuation physical quantities forthese transmission lengths calculated and adjusted by the attenuationphysical quantity calculating and adjusting device.
 3. The tomographicapparatus according to claim 1, wherein the correction functioncalculating device calculates the correction function by obtaining thecorrection function by a least square method using the ratios betweenmeasured attenuation physical quantities for at least two transmissionlengths measured by the attenuation physical quantity measuring device,and calculated attenuation physical quantities for these transmissionlengths calculated and adjusted by the attenuation physical quantitycalculating and adjusting device.
 4. The tomographic apparatus accordingto claim 1, wherein both the filter length calculating device and thecorrection function calculating unit use a measured attenuation physicalquantity for one transmission length of measured attenuation physicalquantities for at least two transmission lengths measured by theattenuation physical quantity measuring device.